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<a name="safe_numerics.tutorial.3"></a>Arithmetic on Unsigned Integers Can Yield Incorrect Results</h3></div></div></div>
<p>Subtracting two unsigned values of the same size will result in an
    unsigned value. If the first operand is less than the second the result
    will be arithmetically in correct. But if the size of the unsigned types
    is less than that of an <code class="computeroutput">unsigned int</code>, C/C++ will promote the
    types to <code class="computeroutput">signed int</code> before subtracting resulting in an
    correct result. In either case, there is no indication of an error.
    Somehow, the programmer is expected to avoid this behavior. Advice usually
    takes the form of "Don't use unsigned integers for arithmetic". This is
    well and good, but often not practical. C/C++ itself uses unsigned for
    <code class="computeroutput">sizeof(T)</code> which is then used by users in arithmetic.</p>
<p>This program demonstrates this problem. The solution is to replace
    instances of built in integer types with corresponding safe types.</p>
<pre class="programlisting"><p><span class="comment">//  Copyright (c) 2018 Robert Ramey</span>
<span class="comment">//</span>
<span class="comment">// Distributed under the Boost Software License, Version 1.0. (See</span>
<span class="comment">// accompanying file LICENSE_1_0.txt or copy at</span>
<span class="comment">// http://www.boost.org/LICENSE_1_0.txt)</span>

<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>

<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">safe_numerics</span><span class="special">/</span><span class="identifier">safe_integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>

<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="keyword">int</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="special">[</span><span class="special">]</span><span class="special">)</span><span class="special">{</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"example 8:"</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"undetected erroneous expression evaluation"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Not using safe numerics"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
    <span class="keyword">try</span><span class="special">{</span>
        <span class="keyword">unsigned</span> <span class="keyword">int</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">127</span><span class="special">;</span>
        <span class="keyword">unsigned</span> <span class="keyword">int</span> <span class="identifier">y</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
        <span class="keyword">unsigned</span> <span class="keyword">int</span> <span class="identifier">z</span><span class="special">;</span>
        <span class="comment">// this produces an invalid result !</span>
        <span class="identifier">z</span> <span class="special">=</span> <span class="identifier">y</span> <span class="special">-</span> <span class="identifier">x</span><span class="special">;</span>
        <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"error NOT detected!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
        <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" != "</span> <span class="special">&lt;&lt;</span> <span class="identifier">y</span> <span class="special">&lt;&lt;</span> <span class="string">" - "</span> <span class="special">&lt;&lt;</span> <span class="identifier">x</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
    <span class="special">}</span>
    <span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">{</span>
        <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"error detected!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
    <span class="special">}</span>
    <span class="comment">// solution: replace int with safe&lt;int&gt;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Using safe numerics"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
    <span class="keyword">try</span><span class="special">{</span>
        <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">safe_numerics</span><span class="special">;</span>
        <span class="identifier">safe</span><span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">127</span><span class="special">;</span>
        <span class="identifier">safe</span><span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">y</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
        <span class="identifier">safe</span><span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">z</span><span class="special">;</span>
        <span class="comment">// rather than producing an invalid result an exception is thrown</span>
        <span class="identifier">z</span> <span class="special">=</span> <span class="identifier">y</span> <span class="special">-</span> <span class="identifier">x</span><span class="special">;</span>
        <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"error NOT detected!"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
        <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">z</span> <span class="special">&lt;&lt;</span> <span class="string">" != "</span> <span class="special">&lt;&lt;</span> <span class="identifier">y</span> <span class="special">&lt;&lt;</span> <span class="string">" - "</span> <span class="special">&lt;&lt;</span> <span class="identifier">x</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
    <span class="special">}</span>
    <span class="keyword">catch</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span> <span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span><span class="special">{</span>
        <span class="comment">// which we can catch here</span>
        <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"error detected:"</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">(</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
    <span class="special">}</span>
    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</p></pre>
<pre class="screen">example 8:undetected erroneous expression evaluation
Not using safe numerics
error NOT detected!
4294967171 != 2 - 127
Using safe numerics
error detected:subtraction result cannot be negative: negative overflow error
Program ended with exit code: 0</pre>
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